VARIABLE NEIGHBORHOOD

PREDICTION OF TEMPORAL

COLLECTIVE PROFILES

Presentation for EuroIoTA ’16

Speaker: Keun-Woo Lim

Telecom Paristech

24-11-2016

Brief Overview

What do we do in this work?

Analysis of temporal collective profiles (time-series)

Use of mobile datasets (cellular, Wi-Fi)

Real–time & Lightweight prediction (online prediction)

What do we try to achieve?

Better prediction accuracy

Lower computational complexity

Better application & use case

Contents

Contents Introduction

Methodology

Prediction

Outlier Detection

Future Work

Introduction

Temporal collective profiles

Representation of data that aggregate behavior of

group of individuals – over time

Can be categorized in various ways

“Daily Profiles”

What are collected?

Basic telephone calls and SMS?

However, we want to focus on more specific matters

Specific application data

Usage of Internet service

Why do we analyze these data?

For “online network analysis”

Real-time prediction of the near-future

Recognition of sudden changes/outliers

Timely adaptation

Use cases

Resource allocation

Traffic handling

Social behavior

Requirements

Low computational complexity

Lightweight prediction methods

Accuracy

Still have to be accurate

Dataset

Cellular mobile dataset

1-week data from 90 lacs in Paris

More than 500 daily profiles

Wi-Fi cloud dataset

122 days (March 1st to June 30th, 2014)

60 million URL connection logs

(Top 20 mobile applications)

Methodology

What should we do with daily profiles?

Daily profiles can be:

Very similar to each other (same day, location, etc.)

Very different too (outlier, events)

We use methods to calculate similarity

Cluster similar profiles

Distinguish different profiles

Previous work (Offline analysis)1

Utilization of clustering methods (UPGMA)

With similarity comparison techniques (DTW, quantiles)

Not ideal in online data analysis

Clustering may take long time (𝑂(𝑀2𝑁3)with DTW)

1K. Lim, S. Secci, L. Tabourier, B. Tebbani, “Characterizing and predicting mobile application usage,”

https://hal.archives-ouvertes.fr/hal-01345824/document

Profile similarity

We use two examples of similarity measures

(M values in a time-series)

Euclidean distance (ED) = Θ(M)

Dynamic time warping (DTW) = Θ(M2)

For specific dataset containing N profiles,

ED = Θ(N2M)

DTW = Θ(N2M2)

to compare all with each other

Weighted graph representation

Using similarity measures, we acquire a graph

structure of neighbors

E.g., if ED is used, lower value = more similar

Filtering paths

Filter neighbors with high distance

Depending on the value of α, the number of neighbors

change for all profiles

Visualization of graph structure

Example graph structure for ED – cellular dataset

Variable Neighborhood Prediction

(VNP)

Principle of VNP

For a new day 𝑥𝑛(𝑡), we configure

𝑡0 = 0, 𝑡1 = 0~24, 𝑡2 = 24 (hour)

Objective

Observation period = 𝑥𝑛 𝑡0, 𝑡1 Create a temporal profile to predict 𝑥𝑛 𝑡1, 𝑡2

Find 𝑥 from the observation period

The closest profile 𝑥, in 𝑥 𝑡0, 𝑡1 and 𝑥𝑛 𝑡0, 𝑡1

Find the neighbors

Using closest neighbor 𝑥, we find the group of

neighbors 𝑁𝑛 to be used for prediction

For any other profile y of the training set,

𝑦 ∈ 𝑁𝑛 𝑖𝑖𝑓𝑠 𝑥𝑛 𝑡0, 𝑡1 , 𝑦 𝑡0, 𝑡1 ≤ 𝑎 ∙ 𝑠 𝑥𝑛 𝑡0, 𝑡1 , 𝑥 𝑡0, 𝑡1

Creating the prediction profile

Using 𝑁𝑛, formulate the prediction

𝑥𝑛 𝑡 =σ𝑦∈𝑁𝑛 𝑠(𝑥𝑛,𝑦)∙𝑦(𝑡)

σ𝑦∈𝑁𝑛 𝑠(𝑥𝑛,𝑦)

Simply put, it is the weighted average over the profiles

of its neighborhood

Training Parameter 𝑎

𝑎 can be tuned to select the optimal number of

neighbors

Variable neighborhood search to find the 𝑎 that yields

the highest accuracy over time

E.g. 1.0 < 𝑎 < 10.0

Drawbacks

Increase in complexity (recalculate for each 𝑎)

Calculating multiple 𝑡1

For a more fine-grained prediction, multiple 𝑡1 can

be used in one day

Repetition of the VNP (e.g. per-hour analysis)

Handling Complexity - VNP

Computation of calculating neighborhood of target day per 𝑎 :

ED = Θ(NM)

DTW = Θ(NM2)

Depending on N, this can be large in practice

Also, in case of multiple 𝑡1 analysis, large M can also impact

Handling Complexity - Graph

Can be heavy

ED = Θ(N2M)

DTW = Θ(N2M2)

Luckily, graph representation is only updated once per day

Although, needed for various M in case of multiple 𝑡1 analysis

Also, space partitioning can be used to reduce time

Via Kd-tree

This can reduce complexity of ED to Θ(log(N)M)

Prediction Analysis

Prediction accuracy analysis

Prediction through relative error, defined as

𝜀 =σ𝑡=𝑡1

𝑡2 𝑥𝑛 𝑡 − 𝑥𝑛 𝑡2

σ𝑡=𝑡1

𝑡2 𝑥𝑛 𝑡2

Comparison with closest neighbor (𝑎 =1), UPGMA

𝑡1 = 12

cellular data - ED cellular data - DTW

Effect of changing 𝑡1

Per-hour analysis

The length of observation period may also effect the performance

of prediction

cellular data - ED cellular data - DTW

Time consumption

The required time can be acceptable for both methods in a

per-hour analysis.

However, need caution for DTW when many profiles are used

cellular data - ED cellular data - DTW

Distribution of α

The distribution of optimal α is focused in range [1,2], allowing

us to easily limit the range of α

Distribution of neighbors is heterogeneous, but most are < 20

Conclusion & Future work

Conclusion & Future work

We have proposed a methodology for online

prediction of mobile time-series datasets

Acceptable time for our current dataset

Can be used for other time-series datasets in various

IoT environment

Further studies include

Testing in a bigger scale dataset

Any Questions?

Appendix – Wi-Fi data prediction

Wifi data - ED Wifi data - DTW